Correction to a Theorem on Total Positivity
Printed: Jun 2006
Carl Johan Ragnarsson
Wesley Wai Suen
David G. Wagner
A well-known theorem states that if $f(z)$ generates a PF$_r$
sequence then $1/f(-z)$ generates a PF$_r$ sequence. We give two
which show that this is not true, and give a correct version of the theorem.
In the infinite limit the result is sound: if $f(z)$ generates a PF
sequence then $1/f(-z)$ generates a PF sequence.
total positivity, Toeplitz matrix, Pólya frequency sequence, skew Schur function
15A48 - Positive matrices and their generalizations; cones of matrices
15A45 - Miscellaneous inequalities involving matrices
15A57 - Other types of matrices (Hermitian, skew-Hermitian, etc.)
05E05 - Symmetric functions and generalizations